My next three weeks are slammed with opportunities, via conferences and teacher trainings, to work with fellow teachers, learn from them, and share resources and thoughts about what I'm most passionate about in math education. The great thing about this two-way learning environment is that it will make me even stronger and better equipped for the upcoming school year as I support my fellows in their classroom.
If we're at the same conference or teacher training, you will be hearing me drive home the importance of the following three challenges we face as teachers of students and students of teachers:
Problem solving
Student thinking
Number sense
Why are these three challenges so important?
Why am I so passionate about lesson design and tech tools that meaningfully support these three challenges?
What resources are available to teachers to support students?
How do we implement said resources to support problem solving, student thinking, and number sense?
At the end of our time together during a workshop or conference, I hope you become better equipped with strategies, tools, resources, ideas, and inspiration to make them your charges for the upcoming school year.
Thanks in advance for letting me be part of your valuable PD time and for allowing me to absorb your insight and knowledge at the same time.
Some cool stuff happened this week. Well at least I think it was cool.
Monday:
One of my math fellows was observed by other math teachers from our district. He was starting a new unit with rational and irrational numbers, focusing on 8.NS.1 and 2. I might be wrong, but pretty dry stuff… here’s how we spiced it up a little.
We did a pre-assessment using the Post-It Plus app. Yes, my obsession with Post-It notes has gone to a new level: digital. We created a file within the app, posted it on his Haiku calendar, and had the students download the file into their app on their iPad.
Students first worked individually to sort the terms from least to greatest for a few minutes. Since his students are grouped in fours, they then narrowed it down to one iPad screen they thought was most accurate. (Quick demo)
*Reflection: we should have had students paired up first, discuss, and narrow it down to two screens for the entire group. Next, the whole group of four students would discuss and narrow the two iPad screens down to one screen for the group.
Once each group settled on a screen they felt most confident with, they took a screenshot and uploaded their group’s screenshot to the Padlet page my fellow created for them.
My fellow used this Padlet page to assess the overall climate of the class (without teaching them a single thing). He used this real-time data to have some really rich conversations and share-out of ideas from students.
Remember to tell students:
It’s okay if you’re wrong.
Make your best guess.
I just want to see what you already might know.
Flash forward to Friday:
The previous weekend I asked the same fellow what he thought about playing War with rational and irrational terms. Side note: I play a few card games with my young son and one of them is War. My fellow thought the idea was epic. He ran with it. Here how he made it awesome:
2 people played War while the other 2 people recorded and were the judges.
The next round, the roles were switched.
There were 3 rounds.
Each round was 6-10 minutes
He stopped class and made a spectacle whenever two students were at war.
The third and final round was between the winners of the first two rounds.
I asked if I had his permission to share the cards and he said, “Sure.”
Tuesday:
Another fellow asked me to model Stacking Cups in their first period class, which ran less than 45 minutes. My fellow requested I complete the task with students in one period. I explained that I’ve never “finished” the task in one period because there is so much to explore and learn in the task. I respected the request and tried to cram it into one period. I spent too much time launching the task.
Act 2 (the best part) felt rushed and we still didn't finish. My fellow and I debriefed and made some adjustments so she could finish it with her next period. She stuck to the adjustments and did a fantastic job facilitating the task. The students were doing awesome and amazing math during Act 2… and what do you know? The class was over. I love that my fellow was going to revisit the task the next day. Could we have spent another day on the task? Yes. It’s a starting point and I’m very proud of my fellow for trying out something new and doing a great job. I’d say the sweet spot would be one-and-a-half days for this task...
*Side note: I encourage you do styrofoam cups earlier in the year, and use Stacking Cups throughout the entire linear systems unit.
Thursday:
Another teacher wanted me to model Stacking Cups as well. When we sat down to plan, she was totally cool with spending one-and-a-half days on the task. Great news!
I launched the task, used a Padlet page to capture what they noticed. I asked the question, "Where will they tie?" and used a Google form to collect their guesses (see my post on using Google forms to collect student thinking). We gave each group only 4 white styrofoam cups. Students were making tables, or writing equations, or some were even wanting to graph their equations. Interesting note: some students started their table with zero cups having a height of 9.2 centimeters. The teacher had only taught graphing systems, so students were already thinking ahead to substitution. It was awesome. She did a wonderful job facilitating her first 3-Act task. We didn’t finish the task in one period, but it felt right knowing we had another half-day to wrap up the task.
Back to Friday:
After work, I started putting the meat in my upcoming session, Math Mistakes and Error Analysis: Diamonds in the Rough. Although I will be showcasing a couple ways I’ve had success with error analysis with students, I love that I’ll be showcasing some awesome work and contributions from:
Crystal (colleague) and Lynda (fellow) wanted to know more about this. So here's the story:
The previous week, I met with one of my high school fellows who teaches Algebra to freshman. As with all my fellows, it's been an extreme pleasure to work with her because she's hungry for ideas and will take suggestions and run with them. It was so cool to walk into her class this past week and see her running with an idea, again.
She had already taught her students ways to solve linear systems; graphically, substitution, elimination, etc. On this day, she prepared six short videos of her solving linear systems and linear inequalities using Educreations on her iPad. Students were to watch the videos and do error analysis, reporting the following on their handout:
Identify the mistake(s) for each question.
Explain what should have been done.
Fix the mistake and complete the question correctly.
Each video was between 60 and 90 seconds in length. We both discussed what we thought would be most effective for her students and short videos was a must. Have you ever noticed how the majority of Khan videos can be extremely lengthy? Sal Khan usually talks (and repeats himself) while writing things on his digital blackboard. To me, that's a waste of someone's time. It's like you watching me type this blog post while I reread every sentence two or three times, stalling so I can finish typing. Another thing I can't stomach in Khan videos is when he fumbles around searching for colors to write with. Lastly, I find it unfortunate that the videos rarely suggest the viewer to pause and consider what's happening. Here's an example. Sorry, here's a 9+ minute example:
I suggested my fellow pause the recordings often and write the equations "offscreen" when not recording. Then, press record again when she's ready to talk and/or write something important on her screen. She also took advantage of this offscreen time to select different colors in order to emphasize different equations, steps, lines, or shading (linear inequalities).
*See the video structure below with suggested notes and style points.
It took my fellow one prep period on a minimum day to create six videos, a supplemental handout, upload the videos to Educreations, and create hyperlinks on her Haiku page for students to access all the videos. That's super impressive. Talk about an activity with meaningful and HUGE return from an efficient investment in her prep time.
When debriefing with my fellow after class, she was completely ecstatic.
I asked her, "What elements made this awesome?"
She replied:
it was video and new
they liked figuring out someone else's mistake
the videos were short
students could pause, rewind, and start the video over
using Desmos to show a graph of the original equations at the end (comparison)
gave students the idea to use Desmos to check their work/answer
self-pacing
very little hand-raising or students drowning
the videos were easy to make
she passed out the handout and said "go" instead of modeling
the handout had a simple structure
the students did most of work, not the teacher
I love this last element the most. The two of us talked about this specific element the previous week. Now she experienced it first-hand and it's an amazing feeling. As an observer, it was awesome to see the students working hard on a meaningful task and helping each other out so it allows her, the teacher, opportunities to calmly circulate and provide support where necessary.
Student engagement and interest were high. Discussions were plenty and authentic. Students were thriving using thinking skills in the "Analyzing" category of Bloom's Taxonomy or Strategic Thinking category of Webb's Depth of Knowledge. Here's a tip I suggested when I noticed some kids plowing through a video and hadn't caught the mistake: pause and make predictions. The video structure will explain pausing and predicting more.
Video Structure:
Part 1:She takes about 8 seconds to explain her plan
*All of this was written on the screen prior to her pressing record. Style points.
Part 2: Multiply the top equation by (-5) in order to eliminate the x-terms
*Here's where we need to ask students to pause and predict what the top equation will look like after being multiplied by (-5).
Model this for students.
Build "pause and predict" prompts into the video.
Circulate the room and ask students to pause and predict.
SO valuable. Don't skip "pause and predict".
Part 3: Write the new equations "offscreen". Don't record yourself writing these equations.
*Notice the new equation is written in red ink. Style points!
**Pause and predict what it will look like when combining the equations
***Catch the mistake?
Part 4: Combine the two equations.
*Another great use of "offscreen" writing.
Part 5: Find the value of y.
Part 6: Substitute the value of y into one of the original equations.
*Yet, another use of "offscreen" writing here. Part 7: Solve for x this time.
*Ask your students to check for reasonableness.
**Find an alternate way to validate (or invalidate) their conclusion.
Part 8: Insert a screenshot of the system graphed in Desmos.
*Mind grenade: the graph doesn't match the algebraic procedure.
**HUGE style points by inserting a visual representation of the correct answer.
For those of you who don't have 1:1 devices in your schools, no sweat. I still recommend you make a video of some sort. Borrow an iPad from someone. Create an Educreations video for error analysis. Use the tips and techniques mentioned here. Your videos should be less than 90 seconds. Play it to your class. Pause the video to have students make predictions and/or discuss possible errors. I guarantee you, good things will happen.
I've put the elevator speeches to rest. Today's two minute speech went well... I think. As one event concludes, I'm excited to resume my ongoing thoughts about number sense and students.
Working with teachers and students, I can't help but be inundated with thoughts about things I miss, look forward to, and will be challenged with this year in and out of the classroom. However, there's one thing I crave more than anything else, and that's working with students, which usually entails having number sense conversations with students.
Today, I had rich number sense conversations with students in Math 7, Math 8, and high school Algebra classes. As I sit here and put the finishing touches on the slides for my upcoming conference workshop, Get Students to Argue in Class With Number Sense Activities, I can't put to words how valuable it is to allow students to talk about math in math class. That's an oversimplification, but we seriously need to provide our students with opportunities to talk to each other, even argue with each other. Mathematical Practice 3:
Construct viable arguments and critique the reasoning of others.
These nine words may be the most important words in the entire Common Core effort.
Last December at CMC North, I was honored to give an Ignite talk about something I'm passionate about: number sense and student conversations. It's titled: Number Sense: I Don't Like This Game Anymore.
Students are hungry for number sense conversations in math class. I really do believe. If you don't believe me, just put up this picture in your class and ask your students, "How long would it take to use all of that?" Then ask them to convince you of their conclusion.
As October quickly approaches, I look forward to seeing you at an upcoming conference this school year. In the meantime, I hope to post more about number sense.
The first day of school is this coming Wednesday. I've never been two days away from the start of school and done so little preparation. It's weird. It's really weird. Here's why:
Admittedly, I won't terribly miss items four through nine. However, the first three and the last always hold a special place in my math heart.
I'll be one of about fifteen Digital Learning Coaches (DLC) in my district this year. I'll be supporting 8-10 middle school math teachers who volunteered to be a DLC Fellow. Together, we'll be finding ways to integrate technology in their classrooms to meet the needs of their students while providing powerful learning experiences. Every time I look at technology or think about implementing some program, application, or digital tool, I look to ask myself (and the teacher), "will this [digital tool] be a more effective and efficient way for student and teacher to learn mathematics, gather data, assess understanding, or communicate?"
I will be:
frequently in the classroom with students and teachers (thank goodness!)
listening to teacher needs, desires, and goals
building relationships with students and teachers
building number sense with students and teachers
having (mathematical or non-mathematical) conversations with students and teachers
developing/designing lessons
teaching (co-teaching or modeling), if necessary
sharing many of the wonderful resources from you (the MTBOS)
I know I will miss the classroom and having my own students. However, I look forward to designing lessons and testing them out on different students throughout the district. I look forward to learning so many things from both the teachers and students. It'll be an extreme pleasure, honor, and learning experience for me to be working alongside so many different teachers and students.
